Chapter Three:
SL, Truth Tables and the Concepts of Logic

In chapter one, we introduced the basic concepts of logic. But these depended on the somewhat vague notions of a "what is possible" and "what is not possible". So, for example, we said that an argument is valid if and only if it is not possible for its conclusion to be false while its premises are true.

But what is possible is not always easily understood or even well defined.

Still, now that we've introduced SL, we can say just what the concept of possibility is for the context of truth functional logic. This will allow us to precisely define all the basic logical concepts (like that of validity) first set out in chapter one. And it will provide a very straightforward test to see when these concepts correctly apply. For instance, we will provide a means to test whether or not an argument in SL is valid or not.

Start with the introductory tutorials presented below, then print out the reference manual for this chapter (that way you'll have a concise statement of this chapter's details to refer to even when away from the computer.) Finally, and most importantly, carefully work your way through the chapter exercises.

Tutorials for Chapter Three

 1 Truth Tables 2 Full Truth Tables 3 Logical Truth, Falsehood, and Indeterminacy in SL 4 Logical Equivalence in SL 5 Validity and Logical Consistency in SL    Part I: Validity in SL    Part II: Logical Consistency in SL    Part III: Short-cut Tables

Exercises for Chapter Three

3.1ex I Truth Tables (one row)
3.1ex II More Truth Tables (one row)
3.1ex III Tables for Any SL Sentences (one row)

3.2ex I Full Truth Tables (for simple sentences)
3.2ex II Determining Truth Value Assignments
3.2ex III Full Truth Tables (for more complex sentences)
3.2ex IV Multiple Choice (table meaning, #rows)
3.2ex V Full Truth Tables for any SL sentence

3.3ex I Multiple Choice
3.3ex II Tables Judging Single Sentences: Logical Truth, etc.
and check a Guide
3.3ex III More Tables Judging Single Sentences
3.3ex IV Tables to Judge Any Single Sentence

3.4ex I Multiple Choice
3.4ex II Tables Judging Pairs of Sentences: Equivalence
3.4ex III More Tables Judging Pairs of Sentences
3.4ex IV Tables to Judge Any Pair of Sentences

3.5ex I Tables for Validity in SL
3.5ex II Multiple Choice
3.5ex III More Tables for Validity in SL
3.5ex IV Tables to Judge Any SL Argument
3.5ex V Tables for Testing Consistency in SL
3.5ex VI Multiple Choice
3.5ex VII More Tables for Testing Consistency in SL
3.5ex VIII Tables to Judge Any Set of SL Sentences

Review Exercises:Crossword,Informal Proofs I, Informal Proofs II

Printable statement of the exercises.